## Final Answer

## Step-by-step Solution

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We can factor the polynomial $12x^3+13x^2-59x+30$ using the rational root theorem, which guarantees that for a polynomial of the form $a_nx^n+a_{n-1}x^{n-1}+\dots+a_0$ there is a rational root of the form $\pm\frac{p}{q}$, where $p$ belongs to the divisors of the constant term $a_0$, and $q$ belongs to the divisors of the leading coefficient $a_n$. List all divisors $p$ of the constant term $a_0$, which equals $30$

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$1, 2, 3, 5, 6, 10, 15, 30$

Learn how to solve polynomial long division problems step by step online. Simplify the expression (12x^3+13x^2-59x+30)/(4x-5). We can factor the polynomial 12x^3+13x^2-59x+30 using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 30. Next, list all divisors of the leading coefficient a_n, which equals 12. The possible roots \pm\frac{p}{q} of the polynomial 12x^3+13x^2-59x+30 will then be. Trying all possible roots, we found that \frac{5}{4} is a root of the polynomial. When we evaluate it in the polynomial, it gives us 0 as a result.